What is the derivative of 5^{x+3} ?

The derivative of 5^{x+3} is ln(5)*5^{x+3}

What is the first derivative of 5^{x+3} ?

The first derivative of 5^{x+3} is ln(5)*5^{x+3}

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derivative of

5^{x + 3}

ln (5) \cdot 5^{x + 3}

Solution steps

\frac{d}{d x} (5^{x + 3})

Apply exponent rule:

a^{b} = e^{b l n (a)}

5^{x + 3} = e^{(x + 3) l n (5)}

= \frac{d}{d x} (e^{(x + 3) l n (5)})

Apply the chain rule:

e^{(x + 3) l n (5)} \frac{d}{d x} ((x + 3) ln (5))

= e^{(x + 3) l n (5)} \frac{d}{d x} ((x + 3) ln (5))

\frac{d}{d x} ((x + 3) ln (5)) = ln (5)

= e^{(x + 3) l n (5)} ln (5)

e^{(x + 3) l n (5)} = 5^{x + 3}

= ln (5) \cdot 5^{x + 3}

What is the derivative of 5^{x+3} ?
The derivative of 5^{x+3} is ln(5)*5^{x+3}
What is the first derivative of 5^{x+3} ?
The first derivative of 5^{x+3} is ln(5)*5^{x+3}